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Искусство войны (The Art of War)

XESXOR9/2/20263 min read
#crypto#custom#easy#chinese-remainder-theorem-(crt#integer-to-bytes-conversion#xor-decryption-with-recovered-

Искусство войны (The Art of War)

Platform: CUSTOM | Category: Crypto | Type: Challenge | Difficulty: Easy | OS: N/A | **Author: XESXOR Techniques: Chinese Remainder Theorem (CRT) for solving system of congruences, Integer to bytes conversion, XOR decryption with recovered key

Summary

Walkthrough of the CUSTOM Crypto Искусство войны (The Art of War). Task: System of modular congruences with XOR-encrypted flag. Solution: Apply Chinese Remainder Theorem (CRT) to find the key, then XOR decrypt the ciphertext.

Description

На войне все средства хороши. Что насчет криптографии? (In war, all means are good. What about cryptography?)

File task.txt:

x ≡ 7 mod 17
x ≡ 4 mod 23
x ≡ 9 mod 37
x ≡ a mod 14467
cyphertext = flag ^ a = 25183524468752482838730336135334402772668615375346038

Analysis

  1. Task name - "Искусство войны" (The Art of War) - is a reference to Sun Tzu, the Chinese military strategist. This is also a hint towards the Chinese Remainder Theorem (CRT). ‍​‌‌​​‌​​​‌‌​​‌​​​​‌‌​‌​​​​‌‌‌​​‌​​‌‌​​​‌​​‌‌‌​​​​​‌‌​‌‌​​​‌‌​​​​‍

  2. System of congruences - we are given three equations with moduli 17, 23, 37, which are pairwise coprime numbers.

  3. Goal - find x, then calculate a = x mod 14467, and use a as the key for XOR decryption.

Solution

Step 1: Applying CRT

The Chinese Remainder Theorem allows us to find a unique solution x in the range [0, 172337) = [0, 14467):

 python 
from sympy.ntheory.modular import crt

moduli = [17, 23, 37]
remainders = [7, 4, 9]

x, _ = crt(moduli, remainders)
print(f"x = {x}")  # x = 3339

‍​‌‌​​‌​​​‌‌​​‌​​​​‌‌​‌​​​​‌‌‌​​‌​​‌‌​​​‌​​‌‌‌​​​​​‌‌​‌‌​​​‌‌​​​​‍

Step 2: Calculating key a

 python 
a = x % 14467  # a = 3339

Since 17 * 23 * 37 = 14467, and x < 14467, then a = x = 3339.

Step 3: XOR decryption

 python 
cyphertext = 25183524468752482838730336135334402772668615375346038
flag_int = cyphertext ^ a

# Convert to string
flag_bytes = flag_int.to_bytes((flag_int.bit_length() + 7) // 8, 'big')
print(flag_bytes.decode())  # CODEBY{REDACTED}

Full solution script

 python 
#!/usr/bin/env python3
"""
Искусство войны (The Art of War) - hackerlab CTF
Chinese Remainder Theorem + XOR decryption
"""
‍​‌‌​​‌​​​‌‌​​‌​​​​‌‌​‌​​​​‌‌‌​​‌​​‌‌​​​‌​​‌‌‌​​​​​‌‌​‌‌​​​‌‌​​​​‍

from sympy.ntheory.modular import crt

# System of congruences from task.txt
moduli = [17, 23, 37]
remainders = [7, 4, 9]

# Solve using Chinese Remainder Theorem
x, _ = crt(moduli, remainders)
print(f"CRT solution: x = {x}")

# Calculate key a = x mod 14467
# Note: 17 * 23 * 37 = 14467, so a = x
a = x % 14467
print(f"Key a = {a}")

# XOR decrypt the ciphertext
cyphertext = 25183524468752482838730336135334402772668615375346038
flag_int = cyphertext ^ a

# Convert integer to bytes
flag_bytes = flag_int.to_bytes((flag_int.bit_length() + 7) // 8, 'big')
print(f"Flag: {flag_bytes.decode()}")

‍​‌‌​​‌​​​‌‌​​‌​​​​‌‌​‌​​​​‌‌‌​​‌​​‌‌​​​‌​​‌‌‌​​​​​‌‌​‌‌​​​‌‌​​​​‍

Output:

CRT solution: x = 3339
Key a = 3339
Flag: CODEBY{REDACTED}

Theory: Chinese Remainder Theorem

CRT states that if m1, m2, ..., mk are pairwise coprime, then the system:

x ≡ r1 (mod m1)
x ≡ r2 (mod m2)
...
x ≡ rk (mod mk)

has a unique solution modulo M = m1 * m2 * ... * mk.

In this task: M = 17 * 23 * 37 = 14467, which matches the last modulus - this is a hint that the CRT solution is the key we're looking for. ‍​‌‌​​‌​​​‌‌​​‌​​​​‌‌​‌​​​​‌‌‌​​‌​​‌‌​​​‌​​‌‌‌​​​​​‌‌​‌‌​​​‌‌​​​​‍

Key Takeaways / Lessons

  • Mastering Chinese Remainder Theorem (CRT) for solving system of congruences, Integer to bytes conversion, XOR decryption with recovered key was key to this challenge.
  • Always check for common misconfigurations and verify assumptions.

Crafted by XESXOR Research • 2025-12-30 • CUSTOM • Искусство войны (The Art of War) • Difficulty: Easy